According to the captivating new book “Hello Goodbye Hello,” Alexander Woollcott, the writer and Algonquin Circle wit, loved to play a game called Strange Bedfellows. One of his biggest coups took place at a Cap d'Antibes villa in summer 1928, when he succeeded in bringing together Harpo Marx and George Bernard Shaw (“corned beef and roses,” as he called them) at lunch. The two hit it off, and later that week Harpo drove Shaw to Cannes, where a friend of the playwright's cast them as extras in a movie; a scene featuring them playing billiards, alas, would be left on the cutting-room floor.

In “Hello Goodbye Hello,” Craig Brown — a longtime columnist for the satirical British magazine “Private Eye” — weaves together dozens of such encounters into a glittering daisy chain that reads like a mathematical proof of the theory of six degrees of separation.

“Everything in this book is documented,” he writes. “Nothing is invented. When accounts of the same meeting differ, as they almost always do, I have sided with the most likely.”

One of the stranger conceits of “Hello Goodbye Hello” is that it describes 101 meetings and expends exactly 1,001 words on each one, resulting in a work that is 101,101 words long. This mathematical construct lends structure to the volume, though this is the one aspect of the enterprise that feels artificial and contrived — happily, something the reader barely notices so engaging is Brown's narrative.

Brown chooses a straightforward narrative voice that proves as pliant as it is entertaining. In drawing upon an assortment of source material including diaries, biographies, interviews and obituaries, Brown constructs portraits that have all the immediacy of reportage, all the fanciful detail of fiction. He has whipped up a delightful summertime confection — funny, diverting, occasionally wistful.